4 Answers
4

It must be daytime. Only graduates of the Academy are allowed to fly at night; attempting to skydive at night results in the annoying lecture from the Rescue Knight.

Link may only skydive from designated points (usually wooden piers) in Skyloft; falling off anywhere else does not cause him to assume the skydiving posture, and results in the annoying lecture from the Rescue Knight.

You have to dash off the piers. If you don't dash you'll dangle off and you fall off, not dive off. If you are trying to fly at night, as other comments say, you cannot call your Loftwing. One more thing - you have to dive back into Faron Woods, your Loftwing can't fly down with you.